**SUMMA****R****Y**

The second law of thermodynamics leads to the definition of a new property called *ent**r**op**y**, *which is a quantitative measure of microscopic disorder for a system. The definition of entropy is based on the *Clausius inequality, *given by

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*where the equality holds for internally or totally reversible processes and the inequality for irreversible processes. Any quantity whose cyclic integral is zero is a property, and entropy is defined as*

where *S*gen is the *ent**r**op**y generated *during the process. Entropy change is caused by heat transfer, mass flow, and irreversibilities. Heat transfer to a system increases the entropy, and heat transfer from a system decreases it. The effect of irreversibili- ties is always to increase the entropy.

Entropy is a property, and it can be expressed in terms of more familiar properties through the *T ds *relations, expressed as

These two relations have many uses in thermodynamics and serve as the starting point in developing entropy-change relations for processes. The successful use of *T ds *relations de- pends on the availability of property relations. Such relations do not exist for a general pure substance but are available for incompressible substances (solids, liquids) and ideal gases.

The *entropy-change *and *isentropic relations *for a process can be summarized as follows:

The work done during a steady-flow process is proportional to the specific volume. Therefore, u should be kept as small as possible during a compression process to minimize the work input and as large as possible during an expansion process to maximize the work output.

The reversible work inputs to a compressor compressing an ideal gas from *T*1, *P*1 to *P*2 in an isentropic (*P*u*k *= constant), polytropic (*P*u*n *= constant), or isothermal (*P*u = constant) manner, are determined by integration for each case with the following results:

The work input to a compressor can be reduced by using multistage compression with intercooling. For maximum savings from the work input, the pressure ratio across each stage of the compressor must be the same.